Question

Решите уравнение
$9^{x} - { 2 }^{x + 0.5} = {2}^{x + 3.5} - {3}^{2x - 1}$
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Answer 1

Ответ:

x=1.5

Объяснение:

$\displaystyle\\9^x-2^{x+0.5}=2^{x+3.5}-3^{2x-1}\\\\\\9^x+3^{2x-1}=2^{x+3.5}+2^{x+0.5}\\\\\\9^x+\frac{9^x}{3}=2^x*2^3*\sqrt{2} +2^x*\sqrt{2}\\\\\\9^x(1+\frac{1}{3})=2^x*\sqrt{2} *(8+1)\\\\\\9^x*\frac{4}{3} =9*2^x*\sqrt{2}\\\\\\(\frac{9}{2})^x=\frac{9*\sqrt{2} *3}{4} \\\\\\(\frac{9}{2})^x=\frac{9*9^\frac{1}{2} }{2^\frac{3}{2}}\\\\\\(\frac{9}{2})^x=(\frac{9}{2})^\frac{3}{2} \\\\\\x=\frac{3}{2} \\\\\\x=1.5$